Can the cost of the counseling be credited toward child support payments that I make?

Unless you have very unusual provisions in your decree, the counseling is in addition to child support, not instead.

Medical expenses, which counseling falls under, are not part of child support and you cannot apply them to that purpose. Further, courts normally do not let the non-custodial parent decide how support money is to be spent so it is not up to you.

Child support is based off of your income. Counseling is a medical need and is usually addressed on a 50/50 of uninsured amount split. Take your decree to an attorney but the premise of your question is a theory that likely won't work.

You can ask, but no not normally. The cost of counseling will not normally reduce your child support.

You can check if the provision of counseling giving you any credit. It is unlikely to be in your custody order. Also, you and the mother may be able to modify the order by agreement. You should have a lawyer review your court order and speak with you.